Many designers of electronics, fluid dynamics, and other systems wish to predict the behavior of components of these systems to guide design. It is often desirable for designers to predict the behavior of such components subject to conditions associated with materials used to construct the components and environments in which the components operate. For example, a designer of integrated circuits might predict the thermal behavior of a gallium arsenide (GaAs) transistor having submicron geometric features under particular operating and environmental conditions to assess electrical performance, reliability, failure modes, and design feasibility.
As designs for electronics, fluid dynamics, and other systems become increasingly complex and evolve to include components with geometric and temporal features that span numerous orders of magnitude, designers may predict the behavior of these components using various techniques. A known technique for predicting the behavior of a component requires extensive computational resources to numerically solve partial differential equations for a characteristic, such as temperature, for enough points in space and time to adequately resolve the often minute geometric and temporal features. Although limited efforts have been made to relieve the tremendous computational burden associated with such techniques, these efforts have been insufficient. Furthermore, while previous efforts may have attempted to more efficiently address the geometric complexities of the problem, such efforts fail to account for the significant transient behavior that many components experience, for example, in monolithic microwave integrated circuits (MMIC) or other integrated circuits having pulsed mode operation.
Moreover, in addition to ignoring temporal behavior, which is itself a critical deficiency, such techniques are often limited to unrealistically restrictive materials, operating conditions, and environmental factors, neglect surface features and properties that vary in some manner with the characteristic under consideration, and fail to comprehend the reliability penalty that is often associated with wide fluctuations of the characteristic. For example, deleterious effects related to temperature in integrated circuits are exacerbated as geometric features become more dense and operating frequencies increase to meet particular requirements. Since higher operating temperatures can have a significant and negative effect on the electrical performance and reliability of many integrated circuits, accurately and efficiently predicting transient thermal response is crucial to effective circuit design. Current techniques, which do not provide this capability, are therefore inadequate for predicting component behavior in the rapidly evolving telecommunications and electronics fields.